(Test Paper) CBSE Class X Self Evaluation Tests For Mathematics (Linear Equations in two variables)
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Test Paper : CBSE Class X Self Evaluation Tests For Mathematics
(Linear Equations in two variables)
1. Solve for x and y: ax + by
= a – b; bx –
ay = a + b
2. Find the values of p and q for which the following system of linear
equations has infinite number of solutions: 2x – y = 5
(p + q)x – (2q – p)y = p + 2q + 6
3. Solve for x and y: ax + by = 1; bx + ay = 2ab
a2 + b2
4. Solve for x and y: 217x + 131y = 913 ; 131x + 217y = 827
5. A two digit number is obtained by either multiplying the sum of digits
by 8 and adding 1, or by multiplying the difference of the digits by 13
and adding 2. Find the number. How many such numbers are possible?
6. Solve graphically the system of equations: 2x – y = 2; 4x – y = 8.
Also find the co-ordinates of points where the line meets the axis of x.
7. 8 men and 12 boys can finish a piece of work in 10 days, while 6 men
and 8 boys can finish it in 14 days. Find the time taken by 2 boys and 3
men to complete the same work.
8. Students of a class are made to stand in rows. If one student is extra in
a row, there would be two rows less. If one student is less in a row there
would be three rows more. Find the total number of students in the
class.
9. Use a single graph paper and draw the graphs of following equations:
2y – x = 8; 5y – x = 14; y – 2x =1
Obtain the vertices of triangle so obtained.
ANSWERS:
1. x = 1, y = -1, 2. p = q =3 3. x = a , b
1. x = 1, y = -1, 2. p = q =3 3. x = a , b
a2 + b2 a2 + b2
4. x = 3, y = 2
5. 41
6. (3, 4); (1, 0), (2, 0)
7. 14,
280
8. 60
9. (1, 3), (2, 5),
(–4, 2)